The basis \(\lbrace _\alpha \rbrace \)  is complete for vector functions over the unit sphere [1]}, which implies equality of the integrands in the above expression, ,
\(\int \limits _{4 \pi } S̭({r},{r}^{\prime })\cdot F̭_n({r}^{\prime }) = t_nF̭_n({r}).\) 
